Material Covered – Math 215

Material Covered

Topics Covered

Topics covered in Math 215 include the following:

  1. Three dimensional coordinates
  2. Vectors, their basic operations, and geometric significance
  3. Equations of lines, planes, and quadratic surfaces
  4. Parametric curves and their applications (position, velocity, arc length)
  5. Multivariable functions, their graphs and level sets
  6. Partial derivatives and their significance.  Clairaut’s theorem.
  7. Tangent planes, linear approximations, and the total differential
  8. The chain rule and implicit differentiation
  9. Directional derivatives and the gradient vector
  10. Optimization of multivariable functions with and without constraints. Lagrange multipliers
  11. Double integrals and their applications in Cartesian and polar coordinates
  12. Triples integral and their applications in Cartesian, cylindrical, and spherical coordinates
  13. Vector fields (conservative and nonconservative), curl, divergence
  14. Line integrals of fields and functions 
  15. Green’s theorem.  Theorems on conservative fields
  16. Surface integrals of fields and functions
  17. Stokes’ theorem and the divergence theorem

Sample Materials

The course materials for the course are determined by the course coordinator, and therefore subject to change.  They do seek to build students’ understanding of the course material, its connection to real-world applications, and fundamental skills that are intrinsic to the material.  The following are samples of the work expected of students in recent semesters.

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